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We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population's preferences and on the probability distribution over the sets of feasible alternatives that the society will face. Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule, it is known a priori that the subset of feasible alternatives will be a pair. We define a distinct social choice function for each distribution over the feasible subsets. Our rules can be interpreted as distance minimization—selecting the order closest to the population's preferences, using a metric on the orders that reflects the distribution over the possible feasible sets. The distance is the probability that two orders will disagree about the optimal choice from a randomly selected available set. We provide an algorithmic method to compute these metrics in the case where the probability of a given feasible set is a function only of its cardinality.

One of the main problems impeding the evolution of cooperation is partner choice. When information is asymmetric (the quality of a potential partner is known only to himself), it may seem that partner choice is not possible without signaling. Many mutualisms, however, exist without signaling, and the mechanisms by which hosts might select the right partners are unclear. Here we propose a general mechanism of partner choice, "screening," that is similar to the economic theory of mechanism design. Imposing the appropriate costs and rewards may induce the informed individuals to screen themselves according to their types and therefore allow a noninformed individual to establish associations with the correct partners in the absence of signaling. Several types of biological symbioses are good candidates for screening, including bobtail squid, ant-plants, gut microbiomes, and many animal and plant species that produce reactive oxygen species. We describe a series of diagnostic tests for screening. Screening games can apply to the cases where by-products, partner fidelity feedback, or host sanctions do not apply, therefore explaining the evolution of mutualism in systems where it is impossible for potential symbionts to signal their cooperativeness beforehand and where the host does not punish symbiont misbehavior.

We propose a family of measures of difference between ordinal preference relations. The difference between two preferences is the probability that they would disagree about the optimal choice from a random available set. It is in this sense that these measures are choice-based. Measures differ according to the distribution of the random available sets. We use these measures to propose new social choice rules that achieve maximal average assent among the members of the population. We also propose two further applications of these measures. The first is to welfare measurement when choice is irrational. The second is to the measurement of polarization in a population.